The expression “to kill the fatted calf” means: To prepare for a season of rejoicing; to prepare a warm welcome.
The allusion is to the parable of the prodigal son, Luke xv, verses 11 to 32, the younger son who took his portion of his patrimony and journeyed “into a far country, and there wasted his substance with riotous living. And when he had spent all, there arose a mighty famine in that land; and he began to be in want.”
Then, employed as a swineherd, “he would fain have filled his belly with the husks that the swine did eat.”
Finally, coming to his senses, he decided to return home, knowing that his father would at least give him better employment.
“But when he was yet a great way off, his father saw him, and had compassion, and said to his servants, Bring forth the best robe, and put it on him; and put a ring on his hand, and shoes on his feet: And bring hither the fatted calf, and kill it; and let us eat, and be merry: For this my son was dead, and is alive again; he was lost, and is found. And they began to be merry.”